with \(x^1_0=x^2_0=0\) . Inspired by [1]} (or [2]}), we guess that \(z_t^1, \tilde{z}_{(t,e)}^1\)  have the following forms, respectively:
\(z_t^1=\Delta (t)\mathbb {1}_{[\bar{t},\bar{t}+\epsilon ]}+z_t^{1^{\prime }},\quad \tilde{z}_{(t,e)}^1=\tilde{\Delta }(t)\mathbb {1}_{\mathcal {O}}+\tilde{z}_{(t,e)}^{1^{\prime }},\) 
